This document is devoted to explain how the dirinla package deal with random effects. The main idea is to show the idea, depict how it has been implemented, and lastly, show some results.
Let \({\boldsymbol{Y}}\) be a matrix with \(C\) rows and \(N\) columns denoting \(N\) observations for the different categories \(C\) of the \(C\) dimensional response variable \({\boldsymbol{Y}}_{\bullet n} \sim \mathcal{D}({\boldsymbol{\alpha}}_n)\). Let \(\eta_{cn}\) be the linear predictor for the \(n\)th observation in the \(c\)th category, so \({\boldsymbol{\eta}}\) is a matrix with \(C\) rows and \(N\) columns. Let \({\boldsymbol{V}}^{(c)}\), \(c=1, \ldots, C\), represents a matrix with dimension \(N \times J_c\) that contains the covariate values for each individual and each category, so \({\boldsymbol{V}}^{(c)}_{n \bullet}\) shows the covariate values for the \(n\)th observation and the \(c\)th category. Let \({\boldsymbol{\beta}}\) be a matrix with \(J_c\) rows and \(C\) columns representing the regression coefficients in each dimension, then the relationship between the parameters of the Dirichlet distribution and the covariates is set up as: \[\begin{equation}\label{eq:dirichlet_regression} g(\alpha_{cn}) = \eta_{cn} = {\boldsymbol{V}}^{(c)}_{n\bullet} {\boldsymbol{\beta}}^{c} \,\,, \end{equation}\] where \(g(\cdot)\) is the link-function. As \(\alpha_c>0\) for \(c = 1,\ldots,C\), log-link \(g(\cdot) = \log(\cdot)\) is used. {The regression coefficients \({\boldsymbol{\beta}}^{(c)}\) are a column vector with \(J_c\) elements}.
The main idea of this document is to show how we are able to introduce random effects in the formula. To show how it works, we show an example where we include two different random effects. Both are shared by two components. \[\begin{eqnarray}\label{eq:dirichlet_regression2} g(\alpha_{1n}) & = & \eta_{1n} = {\boldsymbol{V}}^{(c)}_{n\bullet} {\boldsymbol{\beta}}^{1} + w^{1}_{n}\,\,, \nonumber \\ g(\alpha_{2n}) & = & \eta_{2n} = {\boldsymbol{V}}^{(c)}_{n\bullet} {\boldsymbol{\beta}}^{2} + w^{1}_{n}\,\,, \nonumber \\ g(\alpha_{3n}) & = & \eta_{3n} = {\boldsymbol{V}}^{(c)}_{n\bullet} {\boldsymbol{\beta}}^{3} + w^{2}_{n}\,\,, \nonumber \\ g(\alpha_{4n}) & = & \eta_{4n} = {\boldsymbol{V}}^{(c)}_{n\bullet} {\boldsymbol{\beta}}^{4} + w^{2}_{n}\,\,, \nonumber \\ \nonumber \\ {\boldsymbol{w}}^{1} & \sim & \mathcal{N}(0, \tau_1) \,, \ {\boldsymbol{w}}^{2} \sim \mathcal{N}(0, \tau_2) \nonumber \\ \end{eqnarray}\]
Previous equation can be rewritten in a vectorized form. In particular, if \[{\boldsymbol{\tilde{\eta}}}= \underbrace{\begin{bmatrix} {\boldsymbol{\eta}}_{\bullet 1} \\ \vdots \\ {\boldsymbol{\eta}}_{\bullet N} \end{bmatrix}}_{CN \times 1} \, \ \] denotes a restructured linear predictor, being \({\boldsymbol{\eta}}_{\bullet n}\) a column vector representing the linear predictor for the \(n\)th observation and all the categories, the model in matrix notation is (without priors): \[\begin{equation}\label{eq:dirichlet_regression_matricial} {\boldsymbol{\tilde{\eta}}} = {\boldsymbol{A}} {\boldsymbol{x}}(\tau_1, \tau_2) \,, \end{equation}\] where \({\boldsymbol{A}}\) is the matrix with covariates properly constructed with \(CN\) rows and j (elements of the latent field) columns and \({\boldsymbol{x}}(\tau_1, \tau_2)\) the elements of the latent Gaussian field. Some of them come from the iid effect and depends on the hyperpars \(\tau_1\) and \(\tau_2\). When we write \({\boldsymbol{\theta}}\) we are refering to the vector \((\sigma_1, \sigma_2)\).
As INLA can not deal with multivariate likelihood, the challenge is measure the effect of the likelihood on the posterior and get \(p( {\boldsymbol{x}} \mid {\boldsymbol{y}})\) and \(p( {\boldsymbol{\theta}} \mid {\boldsymbol{y}})\).
All here depicted is based on the INLA method for non-linear predictors from the inlabru R-package (https://inlabru-org.github.io/inlabru/articles/method.html).
The dirichlet likelihood is approximated by conditional independent gaussian, \({\boldsymbol{\tilde{z}_0}}\) (see https://arxiv.org/pdf/1907.04059.pdf section 4). \[{\boldsymbol{\tilde{z}_0}} \mid {\boldsymbol{\tilde{\eta}}} \sim \mathcal{N}({\boldsymbol{L_{0}}}^T {\boldsymbol{\tilde{\eta}}}, {\boldsymbol{I_{CN}}})\,.\] Then: \[p({\boldsymbol{y}} \mid {\boldsymbol{x}}, {\boldsymbol{\theta}}) = p( {\boldsymbol{y}} \mid \tilde{\eta}) \approx p({\boldsymbol{z}} \mid \tilde{\eta}) = p({\boldsymbol{z}} \mid {\boldsymbol{x}}, {\boldsymbol{\theta}}) \,.\] The model posterior is factorised as: \[p({\boldsymbol{\theta}}, {\boldsymbol{x}} \mid {\boldsymbol{y}}) = p({\boldsymbol{\theta}} \mid {\boldsymbol{y}}) \cdot p({\boldsymbol{x}} \mid {\boldsymbol{y}}, {\boldsymbol{\theta}}) \,,\] and the approximation is factorised as: \[\overline{p}({\boldsymbol{\theta}}, {\boldsymbol{x}} \mid {\boldsymbol{\tilde{z}_0}}) = \overline{p}({\boldsymbol{\theta}} \mid {\boldsymbol{\tilde{z}_0}}) \cdot \overline{p}({\boldsymbol{x}} \mid {\boldsymbol{\tilde{z}_0}}, {\boldsymbol{\theta}}) \,,\]
This section is devoted to explain how the algorithm works. The main function is dirinlareg. One of the key point is that the observation model is linked to \({\boldsymbol{x}}\) only through the linear predictor.`
To show how it works, we are going to do an example step by step.
We use a simple example where we include four different categories with four different covariates and a common random effect, i.e., \[\begin{eqnarray} \log(\alpha_{1n}) & = & \eta_{1n} = \beta_{1}^1 \cdot v_{1n} + w^1(j_n) \,, \nonumber \\ \log(\alpha_{2n}) & = & \eta_{2n} = \beta_{1}^2 \cdot v_{2n} + w^1(j_n) \,, \nonumber \\ \log(\alpha_{3n}) & = & \eta_{3n} = \beta_{1}^3 \cdot v_{3n} + w^2(j_n) \,, \nonumber \\ \log(\alpha_{4n}) & = & \eta_{4n} = \beta_{1}^4 \cdot v_{4n} + w^2(j_n) \,, \nonumber \\ \end{eqnarray}\] where \(v_{kn}\) are covariates \(k = 1, \ldots, 4\) simulated from a random uniform (-1, 1), and \(w^1(j_n)\) and \(w^2(j_n)\) are iid shared random effects. \(j_n = 1, \ldots, J\), being \(J\) the levels of the factor. In the example, we assume that \(J = 25\).
n <- 50
levels_factor <- 25
set.seed(100)
if(is.na(levels_factor)){
levels_factor <- n
}
cat_elem <- n/levels_factor
cat(paste0(n, "-", levels_factor, "\n"))
#Covariates
V <- as.data.frame(matrix(runif((10)*n, -1, 1), ncol=10))
#V <- as.data.frame(matrix(rnorm((10)*n, 0, 1), ncol=10))
names(V) <- paste0('v', 1:(10))
### 4 random effects
iid1 <- iid2 <- rep(1:levels_factor, rep(n/levels_factor, levels_factor))
#Desorder index 3
# pos <- sample(1:length(iid3))
# iid3 <- iid3[pos]
V <- cbind(V, iid1, iid2)
# Formula that we want to fit
formula <- y ~ -1 + v1 + f(iid1, model = 'iid') |
-1 + v2 + f(iid1, model = 'iid') |
-1 + v3 + f(iid2, model = 'iid') |
-1 + v4 + f(iid2, model = 'iid')
names_cat <- formula_list(formula)
x <- c(-1.5, 2,
1, -3)
#random effect
prec_w <- c(4, 9)
(sd_w <- 1/sqrt(prec_w))
w1 <- rnorm(levels_factor, sd = sqrt(1/prec_w[1])) %>% rep(., rep(n/levels_factor, levels_factor))
w2 <- w1
w3 <- rnorm(levels_factor, sd = sqrt(1/prec_w[2])) %>% rep(., rep(n/levels_factor, levels_factor))
w4 <- w2
#w3 <- w3[pos]
x <- c(x, c(unique(w1),
unique(w3)))
d <- length(names_cat)
A_construct <- data_stack_dirich(y = as.vector(rep(NA, n*d)),
covariates = names_cat,
share = NULL,
data = V,
d = d,
n = n )
# Ordering the data with covariates --- ###
eta <- A_construct %*% x
alpha <- exp(eta)
alpha <- matrix(alpha,
ncol = d,
byrow = TRUE)
y_o <- rdirichlet(n, alpha)
colnames(y_o) <- paste0("y", 1:d)
y <- y_o
head(as.data.frame(y))
V[,c(1:4, 11)]
Set the initial point for the latent field
A <- A_construct
x0 <- rep(0, dim(A)[2])
x0
#> [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [39] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0Line search. Note that, in order to do the line search, the A matrix has to be constructed. In the case of the example, is depicted below:
head(A)
#> 6 x 54 sparse Matrix of class "dgCMatrix"
#>
#> [1,] -0.3844678 . . . 1 . . . . . . . . . . . . . .
#> [2,] . -0.3389403 . . 1 . . . . . . . . . . . . . .
#> [3,] . . -0.3451698 . . . . . . . . . . . . . . . .
#> [4,] . . . 0.01017252 . . . . . . . . . . . . . . .
#> [5,] -0.4846550 . . . 1 . . . . . . . . . . . . . .
#> [6,] . -0.6026419 . . 1 . . . . . . . . . . . . . .
#>
#> [1,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [2,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [3,] . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . .
#> [4,] . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . .
#> [5,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> [6,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Line search is run at maximum of 10 iterations, and imposing a condition in the gradient and in the difference of posteriors. The function that do it is look_for_mode_x.
Prepare formula and matrix A to call inla.
Now, the matrix A is just the identity matrix:
d <- 4
data_stack_2 <- data_stack_dirich_formula(y = NA,
covariates = names_cat,
share = NULL,
data = V,
d = d,
n = n )
A <- data_stack_2[[1]]
and the formula is constructed as:
data_stack_2$formula.inla
#> category ~ -1 + f(cat1_v1, model = "linear") + f(cat2_v2, model = "linear") +
#> f(cat3_v3, model = "linear") + f(cat4_v4, model = "linear") +
#> f(iid1, model = "iid") + f(iid2, model = "iid")
#> A = numeric(1)
#> covariates = list(4)
#> covariatesall = list(4)
#> d = numeric(1)
#> data = data.frame(50,13)
#> effects = data.frame(200,6)
#> effects_random = list(2)
#> formula.inla = formula(3)
#> formula.inla.pred = character(1)
#> formula.inla.pred2 = character(1)
#> index_mat = dgeMatrix(8)
#> index_random_names = character(2)
#> n = numeric(1)
#> names_inla_fixed = character(4)
#> random_eff = list(4)
#> random_eff_args = list(4)
#> share = NULL(0)
#> y = logical(1)
being each element incorporated as effect using different index:
data_stack_2[[1]]$effects$data %>% head(.)
Call inla to obtain \(\overline{p}({\boldsymbol{\theta}} \mid {\boldsymbol{\tilde{z}_0}})\) and \(\overline{p}({\boldsymbol{x}} \mid {\boldsymbol{\tilde{z}_0}}) \,,\)
If in step 2, algorithm has converged, we have finished. If not, we define we define a new initial point with the mode of the posterior distributions given by inla.
To conduct the tests, I have simulated different datasets with the following structures. Each dataset has 4 covariates, one per category and a shared random effect. \[\begin{eqnarray} \log(\alpha_{1n}) & = & \eta_{1n} = \beta_{1}^1 \cdot v_{1n} + w^1(j_n) \,, \nonumber \\ \log(\alpha_{2n}) & = & \eta_{2n} = \beta_{1}^2 \cdot v_{2n} + w^1(j_n) \,, \nonumber \\ \log(\alpha_{3n}) & = & \eta_{3n} = \beta_{1}^3 \cdot v_{3n} + w^2(j_n) \,, \nonumber \\ \log(\alpha_{4n}) & = & \eta_{4n} = \beta_{1}^4 \cdot v_{4n} + w^2(j_n) \,, \nonumber \\ \end{eqnarray}\] where \(v_{kn}\) are covariates \(k = 1, \ldots, 4\) simulated from a random uniform (-1, 1), and \(w^1(j_n)\) and \(w^2(j_n)\) are iid shared random effects. \(j_n = 1, \ldots, J\), being \(J\) the levels of the factor.
We simulate datasets with N= 50, 100 and 500; and with different sizes for J. We have fitted the models using Gaussian priors for \(\beta\)s, Half Normal and pc-priors for \(\sigma_1\) and \(\sigma_2\). We are going to fit four different models:
Short-JAGS with Half Normal for standard deviations (mean = 0, sd = 1).
dirinla with pc-priors for standard deviations (sigma = 10, alpha = 0.01).
Long-JAGS with Half Normal for standard deviations (mean = 0, sd = 1).
dirinla with Half Normal for standard deviations (mean = 0, sd = 1).
In order to check the results, we have computed:
Posterior distributions and have compared it.
Computational times
Mean and sd of the fixed effects
Two measures: \(ratio_1\) (closer 0, better is the dirinla fit) and \(ratio_2\) (closer 1, better is the dirinla fit), computed for the parameters and hyperparameters: \[\begin{eqnarray}\label{eq:ratio1_ratio2} ratio_1 & = & (E(\phi_{dirinla}) - E(\phi_{long R-JAGS}))/ SD(\phi_{long R-JAGS}) \,\,, \\ ratio_2 & = & SD(\phi_{dirinla})/ SD(\phi_{long R-JAGS}) \,\,, \end{eqnarray}\]
\(n.eff\) and \(Rhat\) for short and long JAGS.
summary_print <- function(N, J)
{
cat("\n")
cat(sprintf(paste0("#### J = ", J, "\n")))
cat("**Parameters** \n")
cat(paste0("{width=100%}"))
cat("**Hyperparameters** \n ")
cat(paste0("{width=100%} \n \n "))
cat("<br>")
if(N<=500)
{
a <- readRDS("simulation4_50-500.RDS")
}else{
a <- readRDS("simulation4_1000.RDS")
}
a <- a[, c(paste0(N, "-", J))]
#Half normal
# names(a)[c(7,8, 11, 12)] <- c("ratio1_sigma_pc", "ratio2_sigma_pc", "ratio1_sigma_log_hn", "ratio2_sigma_log_hn")
num <- length(a) - 1
names_ele <- names(a)
names(a[[1]]) <- c("JAGS", "dirinla pc", "LONG-JAGS", "dirinla hn")
names(a[c(13,14)]) <- c("res_check_jags", "res_check_long_jags")
for (i in 1:num){
b <- a[i]
if(i == 2)
{
result <- as.numeric(b[[1]]) %>% matrix(., nrow = 4)
colnames(result) <- colnames(b[[1]])
colnames(result) <- c("JAGS_mean", "JAGS_sd", "INLA_PC_mean", "INLA_PC_sd", "LONG_JAGS_mean", "LONG_JAGS_sd", "INLA_HN_mean", "INLA_HN_sd")
rownames(result) <- rownames(b[[1]])
result %>% knitr::kable(., digits = c(4)) %>%
print(.)
}else{
cat(paste0("**", names_ele[i], "** \n "))
b[[1]] %>% as.matrix(.) %>% t(.) %>% knitr::kable(., digits = c(4)) %>% print(.)
cat("\n \n ")
}
}
}
summary_print(N = 50, J = 2)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 86.44 | 24.36 | 4253.34 | 17.89 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.5310 | 0.2567 | -1.5414 | 0.2490 | -1.5315 | 0.2583 | -1.5415 | 0.2489 |
| beta12 | 2.0258 | 0.2145 | 2.0424 | 0.2192 | 2.0254 | 0.2147 | 2.0425 | 0.2190 |
| beta13 | 1.0751 | 0.2111 | 1.0982 | 0.1901 | 1.0766 | 0.2124 | 1.0988 | 0.1900 |
| beta14 | -2.9160 | 0.1876 | -2.9481 | 0.1918 | -2.9203 | 0.1869 | -2.9490 | 0.1916 |
ratio1_beta1_pc
| -0.0382 | 0.0795 | 0.1016 | -0.1486 |
ratio1_beta1_hn
| -0.0388 | 0.0798 | 0.1041 | -0.1533 |
ratio2_beta1_pc
| 0.9246 | 1.0465 | 0.833 | 1.0529 |
ratio2_beta1_hn
| 0.9285 | 1.0509 | 0.8128 | 1.0532 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.0304 | 0.1802 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 1.2871 | 1.1437 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.0142 | 0.1565 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 1.2072 | 1.0707 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.0289 | 0.265 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.7877 | 0.5473 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.0373 | 0.2622 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.7318 | 0.5177 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001 | 1.0009 | 1.0009 | 1.0013 | 1.0009 | 1.0045 | 1.0015 |
| n.eff | 11000.000 | 11000.0000 | 11000.0000 | 5100.0000 | 11000.0000 | 5700.0000 | 3100.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001 |
| n.eff | 5.400e+05 | 3.900e+05 | 2.500e+05 | 5.400e+05 | 5.400e+05 | 2.100e+05 | 61000.000 |
n_levels
| 50-2 |
summary_print(N = 50, J = 5)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 84.7 | 23.86 | 4334.2 | 20.95 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.3347 | 0.2569 | -1.3089 | 0.2479 | -1.3354 | 0.2578 | -1.3089 | 0.2478 |
| beta12 | 1.8220 | 0.2103 | 1.8295 | 0.2188 | 1.8212 | 0.2109 | 1.8287 | 0.2187 |
| beta13 | 0.9425 | 0.1937 | 0.9586 | 0.1866 | 0.9413 | 0.1922 | 0.9582 | 0.1866 |
| beta14 | -2.7211 | 0.2003 | -2.7397 | 0.2008 | -2.7212 | 0.2003 | -2.7391 | 0.2008 |
ratio1_beta1_pc
| 0.103 | 0.0394 | 0.09 | -0.0925 |
ratio1_beta1_hn
| 0.1027 | 0.0357 | 0.0877 | -0.0898 |
ratio2_beta1_pc
| 0.9217 | 1.0824 | 0.976 | 1.0029 |
ratio2_beta1_hn
| 0.9233 | 1.0869 | 0.9576 | 1.0077 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| -0.1074 | 0.0819 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.9862 | 1.1708 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| -0.1145 | -0.0011 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.9156 | 0.9643 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| -0.0769 | 0.0712 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.7606 | 1.0463 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| -0.0707 | 0.0064 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.7238 | 0.9531 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0009 | 1.0009 | 1.0009 | 1.0012 | 1.0015 | 1.0076 | 1.0009 |
| n.eff | 11000.0000 | 11000.0000 | 11000.0000 | 6600.0000 | 3100.0000 | 1700.0000 | 11000.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 |
| n.eff | 4.400e+05 | 4.300e+05 | 1.200e+05 | 5.400e+05 | 5.400e+05 | 5.400e+05 | 3.800e+05 |
n_levels
| 50-5 |
summary_print(N = 50, J = 10)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 85.13 | 20.62 | 4228.33 | 21.36 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.4256 | 0.2390 | -1.4354 | 0.2252 | -1.4216 | 0.2416 | -1.4361 | 0.2251 |
| beta12 | 2.0345 | 0.2446 | 2.0971 | 0.2188 | 2.0308 | 0.2443 | 2.0976 | 0.2187 |
| beta13 | 0.9472 | 0.1927 | 0.9651 | 0.1888 | 0.9475 | 0.1919 | 0.9651 | 0.1888 |
| beta14 | -2.4796 | 0.2092 | -2.5756 | 0.1860 | -2.4741 | 0.2113 | -2.5755 | 0.1859 |
ratio1_beta1_pc
| -0.0571 | 0.2712 | 0.0919 | -0.4804 |
ratio1_beta1_hn
| -0.06 | 0.2734 | 0.0917 | -0.48 |
ratio2_beta1_pc
| 0.8642 | 0.806 | 1.0062 | 0.7746 |
ratio2_beta1_hn
| 0.8676 | 0.8095 | 0.9824 | 0.7762 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.0376 | 0.543 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.9205 | 0.8862 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.0071 | 0.541 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.8641 | 0.844 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.0603 | 0.5148 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.81 | 0.2177 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.0363 | 0.5179 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.7799 | 0.2086 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0013 | 1.0009 | 1.0009 | 1.0019 | 1.0009 | 1.0013 | 1.0408 |
| n.eff | 4600.0000 | 11000.0000 | 11000.0000 | 2000.0000 | 11000.0000 | 5000.0000 | 140.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 |
| n.eff | 2.500e+05 | 5.200e+05 | 5.400e+05 | 5.400e+05 | 5.400e+05 | 3.400e+05 | 1.200e+05 |
n_levels
| 50-10 |
summary_print(N = 50, J = 25)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 85.43 | 24.51 | 4258.83 | 27.08 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.6670 | 0.2697 | -1.7341 | 0.2513 | -1.6678 | 0.2718 | -1.7340 | 0.2512 |
| beta12 | 1.8052 | 0.2592 | 1.8206 | 0.2346 | 1.8047 | 0.2589 | 1.8205 | 0.2346 |
| beta13 | 0.7890 | 0.2320 | 0.8647 | 0.1921 | 0.7878 | 0.2313 | 0.8645 | 0.1921 |
| beta14 | -3.3133 | 0.2003 | -3.3610 | 0.1944 | -3.3130 | 0.2005 | -3.3609 | 0.1944 |
ratio1_beta1_pc
| -0.244 | 0.0613 | 0.3325 | -0.2394 |
ratio1_beta1_hn
| -0.2435 | 0.0609 | 0.3315 | -0.2388 |
ratio2_beta1_pc
| 0.851 | 0.8254 | 0.7176 | 0.9397 |
ratio2_beta1_hn
| 0.8542 | 0.8296 | 0.7002 | 0.9416 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.2252 | -0.5005 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.9417 | 1.1101 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.2159 | -0.4983 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.913 | 1.086 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.2309 | -0.58 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.5614 | 1.4537 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.2264 | -0.5731 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.5486 | 1.4191 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0011 | 1.001 | 1.0009 | 1.001 | 1.0014 | 1.0021 | 1.0019 |
| n.eff | 8800.0000 | 11000.000 | 11000.0000 | 11000.000 | 3600.0000 | 2600.0000 | 11000.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.0025 | 1.001e+00 |
| n.eff | 5.400e+05 | 5.400e+05 | 5.400e+05 | 5.400e+05 | 1.600e+05 | 19000.0000 | 5.400e+05 |
n_levels
| 50-25 |
summary_print(N = 50, J = 50)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 90.12 | 27.47 | 4452.67 | 26.69 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.9463 | 0.2607 | -2.0426 | 0.2377 | -1.9464 | 0.2603 | -2.0426 | 0.2377 |
| beta12 | 1.9259 | 0.2747 | 1.8217 | 0.2324 | 1.9295 | 0.2749 | 1.8219 | 0.2324 |
| beta13 | 1.2146 | 0.2079 | 1.1080 | 0.1906 | 1.2192 | 0.2071 | 1.1079 | 0.1906 |
| beta14 | -2.9008 | 0.1871 | -2.9768 | 0.1912 | -2.9048 | 0.1874 | -2.9766 | 0.1912 |
ratio1_beta1_pc
| -0.3694 | -0.3921 | -0.5369 | -0.3842 |
ratio1_beta1_hn
| -0.3693 | -0.3914 | -0.5373 | -0.3834 |
ratio2_beta1_pc
| 0.8279 | 0.7178 | 0.8805 | 1.0416 |
ratio2_beta1_hn
| 0.8342 | 0.722 | 0.8595 | 1.0404 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.1322 | 0.1228 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.7792 | 0.7058 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.1243 | 0.1557 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.7624 | 0.6984 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.1718 | 0.256 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.4282 | 0.2914 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.1675 | 0.2815 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.4209 | 0.2743 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0012 | 1.001 | 1.0015 | 1.0013 | 1.0045 | 1.0063 | 1.1323 |
| n.eff | 6500.0000 | 11000.000 | 3000.0000 | 4200.0000 | 540.0000 | 8600.0000 | 58.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.0033 | 1.0013 |
| n.eff | 5.400e+05 | 5.400e+05 | 5.400e+05 | 5.400e+05 | 1.300e+05 | 18000.0000 | 7700.0000 |
n_levels
| 50-50 |
summary_print(N = 100, J = 2)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 182.01 | 16.52 | 8993.8 | 11.66 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.4677 | 0.1781 | -1.4736 | 0.1785 | -1.4648 | 0.1787 | -1.4751 | 0.1785 |
| beta12 | 1.8881 | 0.1324 | 1.8936 | 0.1427 | 1.8885 | 0.1334 | 1.8951 | 0.1426 |
| beta13 | 1.1340 | 0.1761 | 1.1409 | 0.1739 | 1.1352 | 0.1762 | 1.1412 | 0.1738 |
| beta14 | -2.7319 | 0.1718 | -2.7398 | 0.1789 | -2.7313 | 0.1714 | -2.7399 | 0.1788 |
ratio1_beta1_pc
| -0.0487 | 0.0386 | 0.0322 | -0.0496 |
ratio1_beta1_hn
| -0.0576 | 0.0494 | 0.0339 | -0.0502 |
ratio2_beta1_pc
| 0.9851 | 1.1534 | 1.0092 | 1.0859 |
ratio2_beta1_hn
| 0.9967 | 1.1581 | 0.9899 | 1.094 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.3601 | 0.4413 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 2.5098 | 2.9556 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.0087 | -0.0305 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 1.1849 | 1.1101 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.232 | 0.2824 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 1.4307 | 1.4938 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| -0.0153 | -0.0531 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 1.0868 | 1.0724 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001 | 1.001 | 1.0011 | 1.0011 | 1.0009 | 1.0009 | 1.0017 |
| n.eff | 11000.000 | 11000.000 | 7600.0000 | 7400.0000 | 11000.0000 | 11000.0000 | 2400.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 |
| n.eff | 5.400e+05 | 5.400e+05 | 3.900e+05 | 1.400e+05 | 5.400e+05 | 4.800e+05 | 3.900e+05 |
n_levels
| 100-2 |
summary_print(N = 100, J = 5)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 178.59 | 18.83 | 8694.55 | 19.65 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.2893 | 0.1773 | -1.2766 | 0.1717 | -1.2869 | 0.1786 | -1.2767 | 0.1716 |
| beta12 | 2.0838 | 0.1264 | 2.0907 | 0.1327 | 2.0827 | 0.1266 | 2.0907 | 0.1327 |
| beta13 | 0.9483 | 0.1519 | 0.9741 | 0.1549 | 0.9479 | 0.1528 | 0.9743 | 0.1549 |
| beta14 | -3.1886 | 0.1676 | -3.1956 | 0.1537 | -3.1885 | 0.1663 | -3.1960 | 0.1537 |
ratio1_beta1_pc
| 0.0577 | 0.0627 | 0.1712 | -0.043 |
ratio1_beta1_hn
| 0.0573 | 0.0629 | 0.1729 | -0.0454 |
ratio2_beta1_pc
| 0.9132 | 1.1114 | 1.0648 | 0.8516 |
ratio2_beta1_hn
| 0.9188 | 1.1124 | 1.0469 | 0.8568 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| -0.0095 | 0.0769 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 1.0342 | 0.9118 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| -0.0619 | 0.0717 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.8992 | 0.8789 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| -0.0218 | 0.1221 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 1.0689 | 0.7147 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| -0.0639 | 0.122 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.9908 | 0.6975 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001 | 1.0012 | 1.0009 | 1.001 | 1.0011 | 1.001 | 1.0033 |
| n.eff | 11000.000 | 6100.0000 | 11000.0000 | 11000.000 | 7300.0000 | 11000.000 | 4600.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 |
| n.eff | 5.400e+05 | 5.400e+05 | 5.400e+05 | 5.400e+05 | 4.100e+05 | 5.400e+05 | 3.000e+05 |
n_levels
| 100-5 |
summary_print(N = 100, J = 10)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 169.71 | 20.46 | 8523.84 | 20 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.7246 | 0.1731 | -1.7354 | 0.1657 | -1.7267 | 0.1739 | -1.7352 | 0.1657 |
| beta12 | 2.0154 | 0.1287 | 2.0169 | 0.1271 | 2.0127 | 0.1273 | 2.0170 | 0.1270 |
| beta13 | 0.9611 | 0.1545 | 0.9841 | 0.1523 | 0.9611 | 0.1557 | 0.9839 | 0.1523 |
| beta14 | -3.0510 | 0.1638 | -3.0667 | 0.1542 | -3.0537 | 0.1640 | -3.0664 | 0.1542 |
ratio1_beta1_pc
| -0.0496 | 0.0327 | 0.1476 | -0.0791 |
ratio1_beta1_hn
| -0.0485 | 0.0334 | 0.1466 | -0.0776 |
ratio2_beta1_pc
| 0.8974 | 1.0042 | 0.9922 | 0.882 |
ratio2_beta1_hn
| 0.908 | 1.0085 | 0.9732 | 0.889 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.079 | 0.0942 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 1.0579 | 0.993 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| -0.0072 | 0.0783 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.9312 | 0.949 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.0776 | 0.1056 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 1.0395 | 0.9101 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| -0.0022 | 0.0943 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.9683 | 0.8837 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0009 | 1.001 | 1.001 | 1.0013 | 1.0009 | 1.0009 | 1.0013 |
| n.eff | 11000.0000 | 11000.000 | 11000.000 | 4800.0000 | 11000.0000 | 11000.0000 | 5000.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 |
| n.eff | 4.600e+05 | 5.400e+05 | 5.400e+05 | 5.400e+05 | 5.400e+05 | 5.400e+05 | 5.400e+05 |
n_levels
| 100-10 |
summary_print(N = 100, J = 25)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 171.42 | 21.07 | 8552.03 | 16.39 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.4289 | 0.1759 | -1.4926 | 0.1636 | -1.4268 | 0.1769 | -1.4926 | 0.1636 |
| beta12 | 2.0190 | 0.1362 | 2.0410 | 0.1262 | 2.0218 | 0.1354 | 2.0413 | 0.1262 |
| beta13 | 1.0814 | 0.1606 | 1.1473 | 0.1533 | 1.0818 | 0.1605 | 1.1472 | 0.1533 |
| beta14 | -3.0197 | 0.1655 | -3.0657 | 0.1471 | -3.0195 | 0.1669 | -3.0652 | 0.1471 |
ratio1_beta1_pc
| -0.3719 | 0.1425 | 0.4081 | -0.2773 |
ratio1_beta1_hn
| -0.3717 | 0.1443 | 0.4075 | -0.2737 |
ratio2_beta1_pc
| 0.8482 | 0.8739 | 0.9473 | 0.7757 |
ratio2_beta1_hn
| 0.8558 | 0.8792 | 0.9262 | 0.7798 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.1888 | 0.8524 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 1.0002 | 0.7479 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.1554 | 0.8476 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.9636 | 0.7346 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.1933 | 0.6323 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.9173 | 0.2027 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.163 | 0.6306 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.8966 | 0.1998 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001 | 1.0009 | 1.0009 | 1.0009 | 1.0013 | 1.001 | 1.0157 |
| n.eff | 11000.000 | 11000.0000 | 11000.0000 | 11000.0000 | 5100.0000 | 11000.000 | 580.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001 | 1.001e+00 | 1.0083 |
| n.eff | 2.000e+05 | 5.400e+05 | 3.600e+05 | 5.400e+05 | 73000.000 | 5.400e+05 | 4000.0000 |
n_levels
| 100-25 |
summary_print(N = 100, J = 100)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 178.87 | 23.08 | 9050.28 | 23.94 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.7892 | 0.1922 | -1.7381 | 0.1640 | -1.7896 | 0.1929 | -1.7383 | 0.1640 |
| beta12 | 2.2428 | 0.1538 | 2.2201 | 0.1394 | 2.2419 | 0.1542 | 2.2206 | 0.1393 |
| beta13 | 1.1452 | 0.1699 | 1.0795 | 0.1566 | 1.1456 | 0.1678 | 1.0788 | 0.1566 |
| beta14 | -3.0647 | 0.1783 | -3.1410 | 0.1583 | -3.0678 | 0.1769 | -3.1401 | 0.1584 |
ratio1_beta1_pc
| 0.267 | -0.1416 | -0.3943 | -0.4137 |
ratio1_beta1_hn
| 0.266 | -0.1386 | -0.3983 | -0.4086 |
ratio2_beta1_pc
| 0.72 | 0.8248 | 0.9083 | 0.8039 |
ratio2_beta1_hn
| 0.7199 | 0.8275 | 0.8803 | 0.8013 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.4395 | 0.2891 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.6985 | 0.5968 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.4262 | 0.2969 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.6889 | 0.5892 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.4385 | 0.3258 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.5128 | 0.2043 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.4277 | 0.3313 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.5082 | 0.2006 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0016 | 1.0014 | 1.0029 | 1.001 | 1.0038 | 1.0016 | 1.0166 |
| n.eff | 2600.0000 | 4000.0000 | 970.0000 | 11000.000 | 670.0000 | 2800.0000 | 160.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001 | 1.001e+00 | 1.001 | 1.001e+00 | 1.0012 |
| n.eff | 5.400e+05 | 5.400e+05 | 73000.000 | 5.400e+05 | 61000.000 | 3.400e+05 | 11000.0000 |
n_levels
| 100-100 |
summary_print(N = 500, J = 2)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 857.67 | 22.91 | 43141.23 | 16.48 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.4931 | 0.0622 | -1.4950 | 0.0649 | -1.4934 | 0.0623 | -1.4948 | 0.0649 |
| beta12 | 2.0117 | 0.0611 | 2.0134 | 0.0597 | 2.0116 | 0.0611 | 2.0131 | 0.0597 |
| beta13 | 1.0572 | 0.0566 | 1.0593 | 0.0576 | 1.0581 | 0.0569 | 1.0593 | 0.0576 |
| beta14 | -3.0679 | 0.0557 | -3.0696 | 0.0555 | -3.0680 | 0.0563 | -3.0696 | 0.0555 |
ratio1_beta1_pc
| -0.0246 | 0.0301 | 0.0205 | -0.0277 |
ratio1_beta1_hn
| -0.0216 | 0.0255 | 0.021 | -0.028 |
ratio2_beta1_pc
| 1.0802 | 0.9736 | 1.0439 | 0.98 |
ratio2_beta1_hn
| 1.0894 | 0.9838 | 1.0204 | 0.9751 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.9784 | 0.6641 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 4.6735 | 3.6745 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.0533 | 0.0854 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 1.1097 | 1.1906 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.6877 | 0.4716 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 1.7296 | 1.4915 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.0522 | 0.0868 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 1.0059 | 0.9952 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0011 | 1.001 | 1.001 | 1.0009 | 1.001 | 1.0016 | 1.0013 |
| n.eff | 8700.0000 | 11000.000 | 11000.000 | 11000.0000 | 11000.000 | 2700.0000 | 4700.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 |
| n.eff | 4.800e+05 | 5.400e+05 | 3.400e+05 | 4.900e+05 | 5.400e+05 | 5.400e+05 | 2.300e+05 |
n_levels
| 500-2 |
summary_print(N = 500, J = 5)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 895.82 | 26.27 | 44329.66 | 24.28 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.4669 | 0.0624 | -1.4687 | 0.0626 | -1.4674 | 0.0618 | -1.4687 | 0.0626 |
| beta12 | 1.9733 | 0.0576 | 1.9753 | 0.0568 | 1.9742 | 0.0581 | 1.9753 | 0.0568 |
| beta13 | 0.9054 | 0.0614 | 0.9071 | 0.0639 | 0.9057 | 0.0620 | 0.9071 | 0.0639 |
| beta14 | -2.9685 | 0.0599 | -2.9706 | 0.0588 | -2.9693 | 0.0592 | -2.9705 | 0.0588 |
ratio1_beta1_pc
| -0.0206 | 0.0189 | 0.0226 | -0.0211 |
ratio1_beta1_hn
| -0.0211 | 0.0197 | 0.0222 | -0.0194 |
ratio2_beta1_pc
| 1.0194 | 0.9675 | 1.0809 | 0.9859 |
ratio2_beta1_hn
| 1.0309 | 0.9902 | 1.0637 | 0.9901 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.2251 | -0.0265 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 1.3176 | 0.7906 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.0287 | -0.0144 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.9427 | 0.7998 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.2123 | -0.0064 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 1.1331 | 0.9152 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.0393 | 0.0076 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.9575 | 0.9155 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0011 | 1.001 | 1.0009 | 1.001 | 1.0009 | 1.0009 | 1.0009 |
| n.eff | 7300.0000 | 11000.000 | 11000.0000 | 11000.000 | 11000.0000 | 11000.0000 | 11000.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001 | 1.001e+00 |
| n.eff | 5.100e+05 | 5.400e+05 | 5.400e+05 | 4.100e+05 | 5.400e+05 | 93000.000 | 3.100e+05 |
n_levels
| 500-5 |
summary_print(N = 500, J = 10)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 859.89 | 27.76 | 43231.97 | 24.61 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.5244 | 0.0609 | -1.5291 | 0.0614 | -1.5246 | 0.0614 | -1.5291 | 0.0614 |
| beta12 | 2.0027 | 0.0570 | 2.0042 | 0.0574 | 2.0028 | 0.0570 | 2.0043 | 0.0574 |
| beta13 | 0.9601 | 0.0632 | 0.9613 | 0.0629 | 0.9596 | 0.0634 | 0.9613 | 0.0629 |
| beta14 | -3.0030 | 0.0575 | -3.0072 | 0.0577 | -3.0035 | 0.0577 | -3.0072 | 0.0577 |
ratio1_beta1_pc
| -0.0738 | 0.0245 | 0.027 | -0.0642 |
ratio1_beta1_hn
| -0.0743 | 0.025 | 0.0268 | -0.0633 |
ratio2_beta1_pc
| 0.9969 | 1.0323 | 1.0038 | 1.0101 |
ratio2_beta1_hn
| 1.0069 | 1.0457 | 0.9799 | 1.0075 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.0534 | -0.0205 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.9511 | 0.8939 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.013 | -0.0113 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.893 | 0.8955 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.0615 | -0.0136 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.9726 | 0.9556 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.0234 | -0.0033 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.9374 | 0.9526 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0016 | 1.0011 | 1.001 | 1.001 | 1.001 | 1.0009 | 1.0009 |
| n.eff | 2500.0000 | 8800.0000 | 11000.000 | 11000.000 | 11000.000 | 11000.0000 | 11000.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 |
| n.eff | 5.400e+05 | 5.400e+05 | 2.300e+05 | 5.400e+05 | 5.400e+05 | 4.500e+05 | 5.400e+05 |
n_levels
| 500-10 |
summary_print(N = 500, J = 25)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 861.24 | 24.5 | 43212.64 | 22.48 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.5330 | 0.0655 | -1.5410 | 0.0636 | -1.5340 | 0.0654 | -1.5410 | 0.0636 |
| beta12 | 2.0678 | 0.0599 | 2.0721 | 0.0578 | 2.0672 | 0.0596 | 2.0721 | 0.0578 |
| beta13 | 1.0241 | 0.0625 | 1.0294 | 0.0616 | 1.0242 | 0.0626 | 1.0294 | 0.0616 |
| beta14 | -3.0033 | 0.0621 | -3.0137 | 0.0583 | -3.0044 | 0.0617 | -3.0137 | 0.0583 |
ratio1_beta1_pc
| -0.107 | 0.0808 | 0.0835 | -0.15 |
ratio1_beta1_hn
| -0.1071 | 0.0811 | 0.0835 | -0.1498 |
ratio2_beta1_pc
| 0.9402 | 0.9586 | 0.9846 | 0.9014 |
ratio2_beta1_hn
| 0.9513 | 0.9736 | 0.9605 | 0.8968 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.029 | 0.0559 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.9632 | 0.9682 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.0184 | 0.0596 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.9482 | 0.9666 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.0322 | 0.0603 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.973 | 0.9628 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.0223 | 0.0642 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.9618 | 0.9599 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001 | 1.001 | 1.0009 | 1.0009 | 1.0012 | 1.001 | 1.001 |
| n.eff | 11000.000 | 11000.000 | 11000.0000 | 11000.0000 | 6700.0000 | 11000.000 | 11000.000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 |
| n.eff | 3.700e+05 | 5.400e+05 | 5.400e+05 | 5.400e+05 | 5.400e+05 | 2.000e+05 | 5.400e+05 |
n_levels
| 500-25 |
summary_print(N = 500, J = 500)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 918.89 | 27.8 | 46139.69 | 28.42 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.3821 | 0.0727 | -1.4206 | 0.0655 | -1.3825 | 0.0725 | -1.4206 | 0.0655 |
| beta12 | 2.0684 | 0.0657 | 2.1061 | 0.0610 | 2.0676 | 0.0655 | 2.1062 | 0.0610 |
| beta13 | 1.1385 | 0.0673 | 1.1908 | 0.0621 | 1.1382 | 0.0669 | 1.1907 | 0.0621 |
| beta14 | -2.9930 | 0.0659 | -3.0641 | 0.0601 | -2.9924 | 0.0647 | -3.0640 | 0.0601 |
ratio1_beta1_pc
| -0.5255 | 0.5879 | 0.7854 | -1.1078 |
ratio1_beta1_hn
| -0.5261 | 0.589 | 0.7848 | -1.107 |
ratio2_beta1_pc
| 0.8076 | 0.8833 | 0.862 | 0.8466 |
ratio2_beta1_hn
| 0.8221 | 0.9023 | 0.8802 | 0.8727 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.8772 | 0.9221 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.7798 | 0.6977 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.8729 | 0.9265 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.7774 | 0.6959 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.8458 | 0.8105 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.6344 | 0.4132 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.842 | 0.8141 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.633 | 0.4116 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0013 | 1.0011 | 1.001 | 1.001 | 1.0019 | 1.0022 | 1.0135 |
| n.eff | 5100.0000 | 7300.0000 | 11000.000 | 11000.000 | 1900.0000 | 1500.0000 | 170.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001 |
| n.eff | 5.400e+05 | 5.400e+05 | 5.400e+05 | 3.700e+05 | 1.100e+05 | 1.800e+05 | 39000.000 |
n_levels
| 500-500 |
summary_print(N = 1000, J = 2)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 1922.16 | 42.31 | 92315.65 | 32.39 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.5430 | 0.0433 | -1.5443 | 0.0446 | -1.5437 | 0.0432 | -1.5443 | 0.0446 |
| beta12 | 2.0529 | 0.0422 | 2.0535 | 0.0421 | 2.0523 | 0.0422 | 2.0536 | 0.0421 |
| beta13 | 1.0588 | 0.0458 | 1.0592 | 0.0461 | 1.0585 | 0.0459 | 1.0592 | 0.0461 |
| beta14 | -3.0300 | 0.0417 | -3.0305 | 0.0423 | -3.0298 | 0.0419 | -3.0305 | 0.0423 |
ratio1_beta1_pc
| -0.014 | 0.0299 | 0.0143 | -0.0186 |
ratio1_beta1_hn
| -0.0143 | 0.0301 | 0.0142 | -0.0184 |
ratio2_beta1_pc
| 1.075 | 1.0351 | 1.011 | 1.0286 |
ratio2_beta1_hn
| 1.0819 | 1.0062 | 1.0042 | 0.995 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| -0.0166 | -0.1335 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 1.0868 | 0.7449 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| -4e-04 | -0.0972 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 1.1007 | 0.821 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| -0.0142 | -0.1327 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.9657 | 0.8996 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.0076 | -0.0897 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.9621 | 0.913 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0011 | 1.0009 | 1.0017 | 1.0009 | 1.0012 | 1.0012 | 1.0011 |
| n.eff | 8800.0000 | 11000.0000 | 2500.0000 | 11000.0000 | 5200.0000 | 5200.0000 | 7400.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 |
| n.eff | 2.700e+05 | 5.400e+05 | 4.900e+05 | 4.500e+05 | 4.400e+05 | 3.600e+05 | 3.400e+05 |
n_levels
| 1000-2 |
summary_print(N = 1000, J = 5)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 1841.19 | 38.91 | 93681.92 | 36.81 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.5351 | 0.0455 | -1.5363 | 0.0457 | -1.5346 | 0.0455 | -1.5363 | 0.0457 |
| beta12 | 2.0172 | 0.0430 | 2.0184 | 0.0434 | 2.0173 | 0.0430 | 2.0184 | 0.0434 |
| beta13 | 0.9978 | 0.0460 | 0.9986 | 0.0474 | 0.9975 | 0.0460 | 0.9986 | 0.0474 |
| beta14 | -2.9929 | 0.0436 | -2.9946 | 0.0437 | -2.9932 | 0.0432 | -2.9946 | 0.0437 |
ratio1_beta1_pc
| -0.0376 | 0.0268 | 0.0236 | -0.0323 |
ratio1_beta1_hn
| -0.0373 | 0.0263 | 0.0235 | -0.0324 |
ratio2_beta1_pc
| 1.0159 | 1.0553 | 1.0638 | 1.0275 |
ratio2_beta1_hn
| 1.0172 | 1.0344 | 1.0594 | 1.0102 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| -0.1576 | -0.1273 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.5801 | 0.6254 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| -0.1769 | -0.1686 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.5673 | 0.5666 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| -0.1459 | -0.1147 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.8248 | 0.8557 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| -0.1715 | -0.1606 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.8347 | 0.8307 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0009 | 1.0011 | 1.0009 | 1.001 | 1.0011 | 1.001 | 1.001 |
| n.eff | 11000.0000 | 10000.0000 | 11000.0000 | 11000.000 | 7400.0000 | 11000.000 | 11000.000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 |
| n.eff | 5.400e+05 | 2.600e+05 | 5.400e+05 | 5.400e+05 | 5.400e+05 | 3.100e+05 | 2.700e+05 |
n_levels
| 1000-5 |
summary_print(N = 1000, J = 10)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 1835.19 | 37.55 | 92609.21 | 36.08 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.5071 | 0.0446 | -1.5109 | 0.0461 | -1.5073 | 0.0447 | -1.5109 | 0.0461 |
| beta12 | 2.0590 | 0.0436 | 2.0611 | 0.0437 | 2.0587 | 0.0437 | 2.0611 | 0.0437 |
| beta13 | 1.0171 | 0.0458 | 1.0184 | 0.0465 | 1.0170 | 0.0458 | 1.0183 | 0.0465 |
| beta14 | -3.0966 | 0.0431 | -3.0984 | 0.0434 | -3.0964 | 0.0429 | -3.0984 | 0.0434 |
ratio1_beta1_pc
| -0.0813 | 0.0543 | 0.0299 | -0.0464 |
ratio1_beta1_hn
| -0.0812 | 0.0544 | 0.0298 | -0.0463 |
ratio2_beta1_pc
| 1.0728 | 1.0381 | 1.0282 | 1.0277 |
ratio2_beta1_hn
| 1.0732 | 1.0168 | 1.0313 | 1.0091 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| -0.0662 | -0.0135 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.8348 | 0.8833 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| -0.0459 | -0.0166 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.8509 | 0.8672 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| -0.0601 | -0.0056 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.9315 | 0.9464 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| -0.0388 | -0.007 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.9366 | 0.9316 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0009 | 1.0013 | 1.001 | 1.0009 | 1.0009 | 1.0012 | 1.0014 |
| n.eff | 11000.0000 | 4400.0000 | 11000.000 | 11000.0000 | 11000.0000 | 6800.0000 | 3900.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 |
| n.eff | 1.100e+05 | 2.100e+05 | 4.100e+05 | 5.400e+05 | 5.400e+05 | 3.800e+05 | 5.400e+05 |
n_levels
| 1000-10 |
summary_print(N = 1000, J = 25)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 1801.8 | 37.91 | 90073.21 | 42 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.5101 | 0.0442 | -1.5164 | 0.0448 | -1.5109 | 0.0439 | -1.5164 | 0.0448 |
| beta12 | 2.0039 | 0.0438 | 2.0071 | 0.0428 | 2.0038 | 0.0435 | 2.0072 | 0.0428 |
| beta13 | 0.9910 | 0.0459 | 0.9974 | 0.0463 | 0.9915 | 0.0458 | 0.9974 | 0.0463 |
| beta14 | -3.0299 | 0.0431 | -3.0335 | 0.0430 | -3.0301 | 0.0431 | -3.0335 | 0.0430 |
ratio1_beta1_pc
| -0.1257 | 0.0778 | 0.1301 | -0.08 |
ratio1_beta1_hn
| -0.1258 | 0.0778 | 0.1301 | -0.08 |
ratio2_beta1_pc
| 1.0502 | 1.0081 | 1.024 | 1.0034 |
ratio2_beta1_hn
| 1.0576 | 0.9804 | 1.0197 | 0.9738 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| -0.0224 | -0.0136 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.9503 | 0.9515 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| -0.0174 | -0.0031 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.9443 | 0.9597 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| -0.0209 | -0.0114 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.9798 | 0.9752 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| -0.0151 | -0.001 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.9709 | 0.9797 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0012 | 1.0017 | 1.0011 | 1.0009 | 1.0009 | 1.0018 | 1.0021 |
| n.eff | 6400.0000 | 2300.0000 | 6900.0000 | 11000.0000 | 11000.0000 | 2100.0000 | 1700.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 |
| n.eff | 5.400e+05 | 5.400e+05 | 5.400e+05 | 4.000e+05 | 5.400e+05 | 3.100e+05 | 1.900e+05 |
n_levels
| 1000-25 |
summary_print(N = 1000, J = 1000)
Parameters
Hyperparameters
times
| JAGS | dirinla pc | LONG-JAGS | dirinla hn |
|---|---|---|---|
| 1900.09 | 42.22 | 94202.86 | 45.14 |
| JAGS_mean | JAGS_sd | INLA_PC_mean | INLA_PC_sd | LONG_JAGS_mean | LONG_JAGS_sd | INLA_HN_mean | INLA_HN_sd | |
|---|---|---|---|---|---|---|---|---|
| beta11 | -1.5240 | 0.0494 | -1.5510 | 0.0455 | -1.5239 | 0.0496 | -1.5510 | 0.0454 |
| beta12 | 1.9464 | 0.0492 | 1.9922 | 0.0438 | 1.9455 | 0.0486 | 1.9922 | 0.0438 |
| beta13 | 0.9849 | 0.0492 | 0.9928 | 0.0461 | 0.9845 | 0.0495 | 0.9928 | 0.0461 |
| beta14 | -2.9883 | 0.0477 | -3.0638 | 0.0438 | -2.9884 | 0.0479 | -3.0638 | 0.0437 |
ratio1_beta1_pc
| -0.5465 | 0.9623 | 0.1674 | -1.5717 |
ratio1_beta1_hn
| -0.5464 | 0.9621 | 0.1675 | -1.5716 |
ratio2_beta1_pc
| 0.8414 | 0.8324 | 0.8832 | 0.8317 |
ratio2_beta1_hn
| 0.8686 | 0.8152 | 0.8638 | 0.8161 |
ratio1_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.7773 | 1.3511 |
ratio2_sigma_pc
| sigma1 | sigma2 |
|---|---|
| 0.9059 | 0.9123 |
ratio1_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.7763 | 1.3439 |
ratio2_sigma_hn
| sigma1 | sigma2 |
|---|---|
| 0.9005 | 0.9126 |
ratio1_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.7618 | 1.2624 |
ratio2_sigma_log_pc
| log(sigma1) | log(sigma2) |
|---|---|
| 0.8197 | 0.6906 |
ratio1_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.761 | 1.2561 |
ratio2_sigma_log_hn
| log(sigma1) | log(sigma2) |
|---|---|
| 0.8147 | 0.6918 |
res_check_jags1
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.0009 | 1.001 | 1.0013 | 1.0012 | 1.0028 | 1.001 | 1.0069 |
| n.eff | 11000.0000 | 11000.000 | 5100.0000 | 6400.0000 | 1000.0000 | 11000.000 | 340.0000 |
res_check_jags2
| beta1[1] | beta1[2] | beta1[3] | beta1[4] | deviance | sigma1 | sigma2 | |
|---|---|---|---|---|---|---|---|
| Rhat | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001e+00 | 1.001 | 1.001e+00 | 1.0011 |
| n.eff | 5.400e+05 | 5.400e+05 | 5.400e+05 | 5.400e+05 | 48000.000 | 2.500e+05 | 16000.0000 |
n_levels
| 1000-1000 |